Interpretation of Single-Crystal Vibrational Spectra and Entropy of Pyrope and Almandine Using a Rigid-Ion Lattice-Dynamical Model

For two silicates with the garnet structure, Mg 3 Al 2 Si 3 O 12 (pyrope) and Fe 3 Al 2 Si 3 O 12 (almandine), a rigid-ion lattice-dynamical model provides good agreement with the observed vibrational spectra. On examining the estimates of thermodynamic functions, as derived from the calculated phonon density of states, the agreement of entropy with the calorimetric data reported in the literature is not as satisfactory as that for other garnets. The situation can be notably improved at all temperatures in a most simple way if an order−disorder equilibrium concerning the distribution of the Mg or Fe atoms around their sites is assumed to take place; the variation of such equilibrium with temperature accounts for a sluggish “order−disorder” transition around 100 K.